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%I #21 Jun 13 2015 00:49:22
%S 11,56,67,123,682,15127,76317,91444,167761,930249,20633239,104096444,
%T 124729683,228826127,1268860318,28143753123,141987625933,170131379056,
%U 312119004989,1730726404001,38388099893011,193671225869056,232059325762067,425730551631123
%N Numerators of continued fraction convergents to sqrt(125).
%C From _Johannes W. Meijer_, Jun 12 2010: (Start)
%C The a(n) terms of this sequence can be constructed with the terms of sequence A001946.
%C For the terms of the periodical sequence of the continued fraction for sqrt(125) see A010186. We observe that its period is five. (End)
%H Vincenzo Librandi, <a href="/A041226/b041226.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1364,0,0,0,0,1).
%F From _Johannes W. Meijer_, Jun 12 2010: (Start)
%F a(5n) = A001946(3n+1),
%F a(5n+1) = (A001946(3n+2) - A001946(3n+1))/2,
%F a(5n+2) = (A001946(3n+2) + A001946(3n+1))/2,
%F a(5n+3) = A001946(3n+2),
%F a(5n+4) = A001946(3n+3)/2. (End)
%F G.f.: -(x^9 -11*x^8 +56*x^7 -67*x^6 +123*x^5 +682*x^4 +123*x^3 +67*x^2 +56*x +11) / ((x^2 +4*x -1)*(x^4 -7*x^3 +19*x^2 -3*x +1)*(x^4 +3*x^3 +19*x^2 +7*x +1)). - _Colin Barker_, Nov 08 2013
%t Numerator[Convergents[Sqrt[125], 30]] (* _Vincenzo Librandi_, Oct 31 2013 *)
%Y Cf. A041227, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 08 2013
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